THROUGHPUT OPTIMIZATION FOR WIRELESS DATA TRANSMISSION THESIS. Submitted in Partial Fulfillment. of the REQUIREMENTS for the.

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1 THROUGHPUT OPTIMIZATION FOR WIRELESS DATA TRANSMISSION THESIS Submtted n Partal Fulfllment of the REQUIREMENTS for the Degree of MASTER OF SCIENCE (Telecommuncatons Networks) at the POLYTECHNIC UNIVERSITY by Saket Snha June 00 Advsor Date Department Head Date Copy No.

2 Vta I was born n Patna, Bhar, Inda. I completed my hgh school educaton tll th grade from Delh Publc School, R.K.Puram, New Delh. In 996 my famly moved to the country of opportuntes, Unted States and I completed the rest of my hgh school educaton n New York. I completed my th grade from Bayard Rustn Hgh School for Humantes and was accepted nto Polytechnc Unversty. I was accepted nto the Accelerated BS/MS Honor Program after a successful completon of whch I would be smultaneously awarded Bachelor of Scence and Master of Scence degrees. I chose Computer Engneerng for the Bachelor of Scence degree and Telecommuncaton Networks for the Mater of Scence degree. Durng my educatonal carrer at Polytechnc Unversty I had a number of professonal experences. Durng the freshman year I worked as a tutor n the Offce of Specal Servces and Hgher Educaton Opportunty program. I used to teach the students the fundamental concepts of Programmng n C++ and Chemstry. Durng my sophomore year, I worked as grader for the department of Computer and nformaton scence. The followng summer durng my Junor Year, I worked as an Intern wth Ptney Bowes where I was nvolved n the development of Netscape Plug-n programs and securty ssues n the feld of wreless data transmsson. Durng the past one and half years, I have been substantally nvolved n my thess n whch I have looked at the Optmzaton of the Throughput of wreless data. The research has been done under the able gudance of Dr. Davd J. Goodman, Department Head of ECE Department at

3 Polytechnc Unversty. I worked as a Research Assstant under hm and have done substantal amount of work n the feld of wreless data transmsson.

4 For my famly and frends for ther love and support throughout my lfe v

5 Acknowledgment Frst, I would lke to gve my deep thanks to Dr. Davd J. Goodman for hs constant and generous gudance, help and encouragement for the research study at Polytechnc Unversty. Workng wth hm has been a great pleasure to me. Dr. Goodman s patence and gudance have made hm not only an excellent advsor, but also a frend. I would lke to express my deep grattude to Dr. Elza Erkp, whose wsdom, ntuton, encouragement and generous advsng helped me a lot durng the study of wreless data transmsson. She was of help to me always whenever I needed her and helped n movng along wth my thess from tme to tme. Dr. Elza Erkp s knowledge of nformaton theory was an nvaluable asset to the techncal mert of my work. I would also lke to thank Dr. Phlp Balaban for hs enormous debt, for hs kndness and nspraton and gvng me the opportunty to work wth hm. He was very helpful n teachng me the bascs of wreless data transmssons and furnshed me wth a lot of useful nformaton, whch helped me n movng ahead wth my research and completng my thess successfully. Hs mentorng and gudance s deeply apprecated. Last but not the least, I would lke to thank all my colleagues at Integrated Informaton Systems Laboratory, Rchard Lavery, Mchael Fanberg, Yelena Gelzard, Znan Ln, Vrglo Rodrguez and Seong-Gu Km for creatng an enjoyable and frendly atmosphere for many useful dscussons. I would especally lke to thank Rchard Lavery, Mchael Fanberg, Yelena Gelzard who have been wth me snce my freshman year and who know better than anyone about the rgors of graduate study lfe. They were always there to answer a queston and to get ther comments on new deas I mght have had. v

6 AN ABSTRACT Maxmzng Throughput by Way of Power Control for Wreless Data by Saket Snha Advsor: Dr. Davd J. Goodman Submtted n Partal Fulfllment of the Requrements for the Degree of Master of Scence (Telecommuncatons Networks) June 00 In ths thess, we ntroduce the concept of maxmzng the Throughput of the system whle mantanng optmum sgnal-to-nterference ratos (SIR) by means of optmzng the powers between the termnals nsde the cellular system. We have looked at two knds of cellular networks: network n whch all the termnals operate wth equal prortes and a network n whch dfferent termnals are assgned unequal transmsson prortes and tred to optmze the overall throughput whle mantanng equal sgnal-tonterference rato by way of power control of the transcevers. Power control s essental to the operaton of wreless networks, because each user s power output contrbutes to the nterference experenced by others. Generally, t s desrable to dentfy a choce of power levels, whch optmze certan network metrcs such as the throughput of the CDMA system beng studed. Throughput s hghly dependent on the product of each transcever s nformaton rate by ts frame success probablty. Ths probablty can be reasonable modeled as strctly dependng on the product of two key varables n a CDMA system: Processng Gan and the sgnal to nterference rato (SIR). The maxmum effectve throughput data on a wreless transmsson s drectly related to the channel characterstcs. The throughput of a wreless channel can be maxmzed by mantanng optmum level of sgnal to v

7 nterference rato between the transmtted powers n the system. One lesson of cellular telephone network operaton s that effectve power control s essental n order to promote system qualty and effcency [4]. The operatng ponts n a wreless data communcaton system results n an unfar equlbrum n that users operate wth unequal sgnal-to-nterference ratos. Further, the power control requred to acheve such operatng ponts are more complex than the smple sgnal-to-nterference rato balancng algorthms for voce. v

8 Table of Contents Abstract v Lst of Fgures.. x Lst of Tables. x. Introducton. Abstract... Introducton Background of CDMA systems.. 3. Motvaton and Descrpton of Utlty Functon. 8. Motvaton for ths Research Approach A model of data transmsson over a wreless CDMA network. 9.. The Data Utlty Functon....3 Power Control for Maxmum Utlty/ Dstrbuted Power Control Network Asssted Power Control Throughput Optmzaton usng Power Control and SIR balancng n a Non- Fadng Channel Assumptons and Defntons 9 3. Defnton of Termnal Throughput Lterature used n the Dervaton of Bt Error Rate Dfferent Modulaton Schemes 3.4 Throughput Optmzaton wth No Whte Gaussan Nose n the channel Analyss of the system wth no Gaussan Nose Conclusons 3 4. Throughput Optmzaton n a CDMA network va Power Control n the presence of Whte Gaussan Nose Introducton to Sgnal to Nose Rato v

9 4. Sgnfcance of SNR n Communcaton Channels Analyss of the Plots Analyss of the graph of V versus SNR Conclusons Throughput Maxmzaton n a CDMA network va Power Control of Tranceves wth Dfferent Prortes Introducton Throughput Optmzaton n a Prorty based system Performance Analyss Relatonshp of Informaton Prorty, β to Processng Gan, G Relatonshp between nformaton prorty, β and α Summary, Conclusons and Future Work Concludng Remarks Future Work Works Cted. 7 x

10 Lst of Fgures. DS-CDMA Transmtter Bock Dagram. 4. DS-CDMA Recever Block Dagram Plot of Recever Power levels versus Dstance 3 4. Non-Coherent Detecton of bnary FSK.. 5. Plot of ( Gα) 6. Plot of ( Gα) G f ', α f ', ( α ) G f ', α f ', ( α ) T vs α when G = 0 and β =.. 8 T vs α when G =6 and β = 8 7. Optmzaton of base staton throughput versus α ( β = ) Plot of normalzed throughput versus α (SNR=) Plot of normalzed throughput versus α (SNR=) Plot of normalzed throughput versus α (SNR=5) Plot of normalzed throughput versus α (SNR=0) Plot of normalzed throughput versus α (SNR=50) Plot of normalzed throughput versus α (SNR=00) Plot of normalzed throughput versus SNR Plot of normalzed versus α ( β = ) Plot of normalzed throughput vs α ( β =, G = 8) Plot of normalzed throughput vs α ( β =, G = 9) Plot of normalzed throughput vs α ( β =, G = 6) Relatonshp between Processng Gan and β 6 0. Plot of α opt versus β 65 x

11 . Throughput optmzaton wth respect to α when β = Plot of T ( α ) versus α for β =,, 4, 8 67 Lst of Tables. Dfferent Modulaton Schemes.... Comparson of G and f ( γ ) Maxmum values of Overall Throughput and throughput of ndvdual termnals Relatonshp of Gcrtcaland β 6 5. Relatonshp between β and α opt for correspondng G crtcal 64 x

12 Maxmzng Throughput by Way of Power Control for Wreless Data Saket Snha, Davd J. Goodman Polytechnc Unversty Brooklyn, NY 0 Chapter. Abstract Introducton Power control s essental to the operaton of wreless networks, because each user s power output contrbutes to the nterference experenced by others. Generally, t s desrable to dentfy a choce of power levels, whch optmze certan network metrcs such as the throughput of the CDMA system beng studed. Throughput s hghly dependent on the product of each transcever s nformaton rate by ts frame success probablty. Ths probablty can be reasonable modeled as strctly dependng on the product of two key varables n a CDMA system: Processng Gan and the sgnal to nterference rato (SIR). The maxmum effectve throughput data on a wreless transmsson s drectly related to the channel characterstcs. The throughput of a wreless channel can be maxmzed by mantanng optmum level of sgnal to nterference rato between the transmtted powers n the system. One lesson of cellular telephone network operaton s that effectve power control s essental n order to promote system qualty and effcency [4]. The operatng ponts n a wreless data communcaton system results n an unfar equlbrum n that users operate wth unequal sgnal-to-nterference ratos [4]. Further, the power control requred to acheve such operatng ponts are more complex than the smple sgnal-to-nterference rato balancng

13 algorthms for voce. In ths paper, we ntroduce the concept of maxmzng the throughput of the system whle mantanng optmum sgnal-to-nterference ratos (SIR) by means of optmzng the powers levels between the termnals nsde the cellular system. Chapter gves you general ntroducton about what a CDMA system s and descrbes the functonalty and the role that a CDMA system plays n today s cellular envronments. Chapter begns by descrbng what motvated us to work on the research presented n ths paper and also provdes a bref overvew of the utlty functon that we are tryng to maxmze n my work by maxmzng the throughout of the base staton under the constrants of the power levels of the transmtters n the system. Chapter looks nto optmzng the throughput of a CDMA system usng Power Control and SIR balancng n a non-fadng channel. Chapter 4 looks at a system wth the presence of Whte Gaussan Nose n the channel. Chapter 5 provdes a bref overvew of optmzng the Throughput by way for Power Control n a CDMA system n whch the transcevers are gven dfferent prortes. Chapter 6 ends the thess wth concluson and a word on future work that can be done on the materal studes n ths thess.

14 . Introducton.. Background on CDMA systems: In 989 Code Dvson Multple Access (CDMA) was a radcally new concept n cellular communcatons. Snce then t has ganed wdespread nternatonal acceptance by cellular rado system operators who are attracted by hgh system capacty and servce qualty. CDMA s a form of spread-spectrum, a famly of dgtal communcaton technques that have been used n mltary applcatons for many years. The core prncple of spread spectrum s the use of nose-lke carrer waves, as was suggested decades ago by Claude Shannon []. Instead of parttonng ether spectrum or tme nto dsjont slots each user s assgned a dfferent nstance of the nose carrer. Whle those waveforms are not rgorously orthogonal, they are nearly so []. And, as the name, spread spectrum mples, bandwdths are much wder than that requred for smple pontto-pont communcaton at the same data rate. Orgnally there were two motvatons: a. Ether to resst enemy efforts to jam the communcatons (ant-jam, or AJ), or b. To hde the fact that communcaton was even takng place, sometmes called low probablty of ntercept (LPI). A basc property of the spread spectrum s a substantal ncrease n bandwdth of an nformaton-bearng sgnal, far beyond that needed for basc communcaton. The bandwdth ncrease, whle not necessary for communcaton, can mtgate the harmful effects of nterference, ether delberate, lke a mltary jammer, or nadvertent, lke co- 3

15 channel users. The nterference mtgaton s a well-known property of all spread spectrum systems. However the cooperatve use of these technques n a commercal, non-mltary, envronment, to optmze spectral effcency was a major conceptual advance []. Spread Spectrum systems generally fall nto one of two categores: frequency hoppng (FH) or drect sequence (DS). In both cases synchronzaton of transmtter and recever s requred. Both forms can be regarded as usng a pseudorandom carrer, but they create the carrer of the sgnals n dfferent ways. CDMA cellular systems use a form of drect sequence. Drect sequence s, n essence, multplcaton of a more conventonal communcaton waveform by a pseudonose (PN) ± bnary sequence n the transmtter. Fgure below represents the frequences occuped by the nformaton sgnal and the transmtted sgnal. Fgure : A DS-CDMA Transmtter block dagram A second multplcaton by a replca of the same ± sequence n the recever recovers the orgnal sgnal. The fgure below represents decodng the sgnal at the recever end. 4

16 Fgure : DS-CDMA Recever Block Dagram The nose and nterference, beng uncorrelated wth the PN sequence, become nose-lke and ncrease the bandwdth when they reach the detector. The sgnal-to-nose rato can be enhanced by narrowband flterng that rejects most of the nterference power. It s often sad that the SNR s enhanced by the processng gan of the channel W/R, where W s the spread bandwdth and R s the data rate. Ths s a partal truth. A careful analyss s needed to accurately determne the performance. In IS-95A CDMA W/R = 0 log(.88 MHz/9600Hz) = db for the 9600 bps rate set []. There are two CDMA common ar nterface standards: c. Forward CDMA channel The forward CDMA channel s the cell-to-moble drecton of communcaton. It carres traffc, a plot sgnal, and overhead nformaton. The plot s a spread, but otherwse unmodulated Drect Sequence Spread Spectrum (DSSS) sgnal []. The plot and overhead channels establsh the system tmng and staton dentty. The plot channel also s used n the moble-asssted handoff (MAHO) process as a sgnal strength reference. d. Reverse CDMA channel 5

17 The REVERSE CDMA CHANNEL s the moble-to-cell drecton of communcaton. It carres traffc and sgnalng. Any partcular reverse channel s actve only durng calls to the assocated moble staton, or when access channel sgnalng s takng place to the assocated base staton. Under deal condtons, n a CDMA network users should not nterfere wth one another. In such a network, each user transmts dgtal nformaton by modulatng a waveform sgnature whch unquely dentfes the user. Sgnatures are ether orthogonal or mnmally crosscorrelated. Hence, a correlaton detector tuned to the ntended transmtter s sgnature allows a recever to separate the desred sgnal from those of other smultaneous transmtters. Thus, under deal condtons, mult-user nterference does not exst. However, a typcal wreless channel s far from deal. In such a channel, much mparment affects the transmtted sgnal. In partcular, lack of user s coordnaton (asynchronous transmsson) and mult-path dsrupt the orthogonalty of the users sgnature. Ths stops the correlator from separatng the desred sgnal from those of smultaneous users. Under these condtons, mult-user nterference becomes a hghly detrmental factor to the operaton of a CDMA network. In partcular, t gves rse to the so-called near-far problem: a suffcently powerful nterferer could degrade the recever s performance to an arbtrary degree. 6

18 The above mples that power control s an ssue of paramount mportance to the effcent operaton of CDMA wreless networks, snce, under realstc condtons, each user s power output contrbutes sgnfcantly to the nterference experenced by others. But power s not the only factor that needs to be optmzed n order to get greater network effcency. In general, one would lke to determne a power level for each actve user n the network n such a manner that a sutable measure of network performance, such as the throughput, be optmzed. The system s throughput can sutably be defned as a (possbly weghted) sum of the contrbuton of each transcever. Each transcever s contrbuton to the throughout can be defned as the product of the transcever s nformaton rate by ts frame success probablty. The probablty can be reasonably modeled as strctly dependng on the product of two key varables: a transcever s processng gan (the rato of the avalable bandwdth to the transcever s nformaton rate) and ts sgnal to nterference rato, SIR, (the rato of the transcever s own transmt power to the sum of the nterferng transcever s power plus applcable nose power that exsts n the envronment). In ths thess, we have tred to maxmze the overall throughput of the wreless system by maxmzng the optmzng the power levels of the transcevers n the system. The throughput of the ndvdual transcever s maxmzed based upon the power levels that are operatng at n the system. 7

19 Chapter Motvaton and Descrpton of Utlty Functon. Motvaton for the Research In today s world, the success of cellular phones prompts the wreless communcatons communty to turn ts attenton to other nformaton servces, many of them n the category of Wreless data communcatons. The qualty and bandwdth effcency of wreless communcaton systems depend of effectve power control algorthm. A termnal and base staton need to transmt enough power to delver a useful sgnal to the recever. However, excessve power causes unnecessary nterference to other recevers, and n the case of transmsson from a portable termnal, t drans battery energy faster than necessary. An effectve power control s essental to promote system qualty and effcency. A Network Asssted Power Control (NAPC) technques s used to maxmze utltes for users whle mantanng equal sgnal-to-nterference ratos for all users [4]. The optmzaton s based upon the propertes of the utlty functon for wreless data systems defned as the number of nformaton bts delvered accurately to a recever for each joule of energy expended by the transmtter. A power control system that maxmzes the utlty functon maxmzes the amount of nformaton that can be transmtted by a termnal to the base staton n a cellular system. The goal of the work s to provde a means of achevng a farer (or more equtable) operatng pont and also allow mplementaton of dstrbuted power control usng sgnal-to-nterference rato nonbalancng. The network keeps on broadcastng a common sgnal-to-nterference rato as the target. In a CDMA system, the target sgnal-to-nterference rato depends on the number of users smultaneously transmttng nformaton to a base staton usng the same 8

20 carrer frequency [8]. The number of users present n a system determnes the throughput of the base staton. We fnd that there s a user populaton sze that maxmzes the throughput of the base staton. Ths populaton sze can be vewed as the capacty of a wreless data system. It corresponds to the capacty of a wreless telephone system, defned as the maxmum number of conversatons that a base staton can handle wthn a sgnal-to-nterference rato constrant. The goal of the work s to provde a farer operaton pont and also to mplement dstrbuted power control usng SIR balancng between the transmtters. The avalablty of varable transmsson rates n a cellular network rases the problem of controllng them n the most spectrally effcent way [8]. In a cellular envronment, the transmsson rates are closely related to the sgnal-tonterference (SIRs) and the SIRs can be effectvely controlled by means of power control, whch s addressed n ths paper.. Approach.. A model of data transmsson over a wreless CDMA network In a somewhat general stuaton, a smple model of data transmsson over a CDMA network could be descrbed as follows: In a sngle cell, non-orthogonal codes carry data packets. Packet errors are caused by nterference and nose. A selectve-repeat scheme based on error detectng codes and acknowledgments allows retransmsson of those packets not successfully detected by the base staton. I assume a perfect error detecton at the base staton and error-free transmsson of acknowledgments from the base staton to the transcevers. In ths smple model, the followng quanttes and/or concepts are of nterest: 9

21 N s the number of transcevers transmttng data smultaneously to the base staton. R s s the source rate beng used by the transcever to transmt the data. We assume n our model that the transmsson rates beng used by all the transcevers are constant. R c chps per second s the chp rate of the channel. R G = R C S and s dentfed as the processng gan of the channel. The data s transmtted as packets, each of whch contans L nformaton bts and a total of M>L bts, whch accounts for bts added for error correcton/detecton, as well as other overhead. Of fundamental mportance s the probablty of correct recepton of a packet. Ths probablty depends on the physcal attrbutes of the system, ncludng the bnary modulaton technque beng used, the forward error correcton scheme, the nature of the channel, and the detals of the recever, ncludng ts demodulator, forward error correcton scheme, the decoder and antenna dversty, f any. We assume that these propertes of the physcal layer can be captured va a sngle real-valued functon, whch gves the packet/frame error probablty as a functon of the product of the transcever s processng gan to ts sgnal-to-nterference rato. 0

22 .. The Data Utlty Functon A utlty functon s a measure of the satsfacton experenced by a person usng a product or servce. In the wreless communcaton lterature, QoS s closely related to utlty. The man objectves of the QoS are: low delay and low probablty of error [4]. The utlty functon of wreless data systems s defned as the rato of throughput of the system (number of nformaton bts delvered accurately) to the power transmtted by the R s L, M transcever. The number of bts delvered accurately to the base staton = f ( γ ) where M s the sze of the packet, L s the number of nformaton bts beng transmtted, R s s the transmsson rate of each transcever transmttng n the cellular system beng consdered here and f(γ) s the probablty of successful transmsson or n other words the frame success rate. Wth channel codng the total sze of each packet s M>L bts. The nformaton s transmtted over the network n packets each contanng L bts of nformaton. The utlty (U) of a packet transmsson can be vewed as the rato of the number of bts transferred, to the energy consumed n the transmsson [4]. The number of bts transferred s gven by: Lf (γ ) and the energy consumed n the transmsson s gve by: PM. Our goal s to maxmze the utlty functon by maxmzng the throughput of R the system and by mnmzng the power level receved by the base staton of each transcever n the system. U = RL f(γ ) M P () where the throughput of the packet transmtted by the transcever,, s gven by

23 T = M RL f(γ ) () where (RL/M) s the payload transmsson rate and f ( γ ) s the frame success rate defned as the probablty of recevng the packet correctly. The frame success rate depends on γ, the target sgnal-to-nterference rato (SIR) at the recever. The propertes of f ( γ ) that make t nterestng are: ( ) = f and ( ) f γ P 0 for P = 0. The product of the number of nformaton bts present n the packet (L) and the probablty of successful transmsson represents the expected number of bts receved accurately by the base staton. In a system of N users, each termnal transmts data to a sngle base staton. The recever for termnal receves energy transmtted by all other termnals n the system. The target SIR γ, depends on the power level that each of the transmtters n the system s operatng at and ther dstances from the base staton [7]. In real systems, the sgnal strength at the recever depends on the dstance from the transmtter. In realty, the receved sgnal s nfluenced by myrad detals of the physcal envronment of the transmtter, recever and the space between them. Some of these factors are terran, buldngs, people and vehcles n the sgnal path, antenna characterstcs and the moton of the transmtter and the recever. For a system wth N termnals smultaneously transmttng to a sngle base staton, there s a lot of nterference experenced by a termnal as a result of the other transmssons. A termnal, located at the edge of a cell, experences more nterference from other termnals because t s far away from the base staton and the sgnal strength at the recever of that termnal decreases sgnfcantly. To acheve a target sgnal-tonterference rato, moble users at the cell border have to use the hghest transmt powers. On the other hand, the termnals, whch are close to the base staton, do not have to use

24 much of ther battery power. Fgure 3 represents the graph of the sgnal strength vs dstance, at varous locatons equdstant from the transmtter. Once could observe that the receved sgnal strength exhbts a wde range of values. Fgure 3 also llustrates that as the dstance decreases, the sgnal strength of the transmtter ncreases and ths s the exact reasonng for why do the termnals close to the base staton have to transmt at a lower power as compared to termnal that are far away from the base staton. Thus, system capacty becomes a very mportant ssue n maxmzng the overall performance of the system. Thus, power control s needed to overcome the near far problem. Ths s how power control works n speech analyss but for dgtal data t s qute dfferent. Fgure 3: Plot of receved power versus dstance (m) 3

25 ..3 Power Control for Maxmum Utlty/ Dstrbuted Power Control In our research, we consder a sngle cell of a CDMA wreless data system wth N termnals transmttng ther data to the same base staton. The path gan of termnal to the base staton s defned as h, =,,, N. The SIR experenced by termnal s defned as: γ = N j j= GP h P h j j + σ = N j= j GQ Q j + σ (3) where G s the CDMA processng gan and s defned as R R channel source. P s the transmtted power of termnal, and σ s the nose power n the base staton recever. The dstrbuted power control problem seeks an algorthm n whch each termnal uses ts local nformaton about ts transmsson to choose power levels that maxmzes the utlty functon of each termnal n the CDMA system. Thus, each termnal n the system tres to acheve the target SIR by perodcally learnng about ts current SIR and then adjustng ts power to reach the equlbrum, assumng that all other termnals n the system mantan ther power levels constant. The maxmum utlty occurs at a power level for whch the partal dervatve of U wth respect to P s zero: U = 0 (4) P We observe n Equaton (4) that n order to dfferentate U wth respect to P, we need to know the partal dervatve of γ wth respect to P. Takng the partal dervatve of γ wth respect to P : 4

26 γ P = N j= j Gh P h j j + σ = γ p (5) Referrng to Equaton () and (5), we can express the dervatve of utlty wth respect to power as: U P = ( γ ) LR f γ ( ) f γ (6) MP γ Therefore, wth P >0, the necessary condton for termnal to maxmze the utlty s ( γ ) f γ f ( γ ) = 0 (7) γ We adopt a notaton γ = γ * for a sgnal to nterference rato that satsfes equaton (7) and we call ths the equlbrum SIR. Once ths equlbrum s reached, all the transcevers n the wreless system operate wth the same SIR, * γ, the soluton to Equaton (7). What needs to be examned s whether equal SIR s the best thng to do and whether the base staton throughout be optmzed under such condtons. In the case of powers that represent the soluton to Equaton (7), we can show that there are power reducton factors α < such that all termnals can ncrease ther utlty to U > ' * U by smultaneously reducng ther transmtted powers from * P to P = α [4]. The power reducton causes ' * P all the termnals to operate at a common SIR ' γ < γ *. Ths n turn results n lower value of f(γ) n Equaton. However, wth respect to utlty, the advantage of a lower power outweghs the dsadvantage of a lower value of f(γ). 5

27 .3 Network Asssted Power Control In the Network Asssted Power Control, a termnal nvolved n the cellular envronment perodcally learns about the current sgnal-to-nterference rato γ and adjusts ts power to am for γ T [4]. Thus f the power of the termnal s P, the adjusted power level s P γ γ T. Ths affects the SIR of other termnals n the system and causes them to change ther power levels [4]. When all the termnals operate wth the same SIR, ther sgnals arrve at the base staton wth the same power level, P rec. Thus, for balanced sgnal-tonterference rato: P h = P f or =,,,N (8) rec In our study of wreless data transmsson, we seek a value of? T that produces the optmum results wth respect to the utlty functon gven n Equaton (). Thus wth? =? T for =,,,N, GP rec γ T = ( N ) Prec + σ (9) P rec = γ Tσ G ( N ) γ T for all (0) By referrng to Equaton () and substtutng Equaton (0) n t, we can derve an expresson for the utlty functon n terms of the common sgnal-to-nterference ratoγ T : U G ( γ ) ( LR h = f N ) T M σ γ T () 6

28 It could be seen from the equaton above that the utlty of termnal s proportonal to the path gan, h. If we consder, the proportonalty factor to be a constant, the target SIR defned as γ T affects the termnals n the same way for all termnals. Therefore, the utlty functon of each termnal s maxmzed once they have acheved the target SIR, γ T. If we adopt the notaton, γ opt, as the maxmzng value of? T, we can fnd the value of γ opt by dfferentatng Equaton () and settng the dervatve equal to zero. When we dfferentate Equaton () wth respect to γ T, we obtan the followng result: Gf ( γ ) [ G ( N )γ ] T df ( γ ) T = T γ T () dγ T Thus, the optmum sgnal-to-nterference rato, γ opt s a soluton to Equaton (). Just lke γ *, the equlbrum SIR, γ opt s dependent on the functon f(γ), whch descrbes the dependence of frame success rate on sgnal to nterference rato. Note that γ opt, unlke γ * depends on the number of the users n the system and also the processng gan of the CDMA system. Therefore, n contrast to the dstrbuted power control scheme wth a target γ T =γ *, the Network Asssted Power Control algorthm ams for γ T =γ opt, the soluton to Equaton (). Also note that γ opt, changes constantly as the users come and leave the system. To keep the termnals nformed about the changes of the optmum SIR, the base staton communcates wth the termnal on the slow assocated control channel that exsts n the wreless systems, and transmts the optmum value of SIR perodcally so that the termnals are nformed about the changng levels and they could change ther power levels accordngly []. Accordng to the lterature, the maxmum number of users a 7

29 CDMA system can support smultaneously under the condtons descrbed above s gven by: G N = γ T + (3) Note that Equaton (3) represents the channel capacty of a CDMA system. Wth G beng constant, we can see that as N grows, the target SIR, γ T, must decrease n order to compensate for the ncrease n N. Also, note that when N =, there s only one termnal n the cellular system and Equaton () reduces to Equaton (7). Therefore, the lone termnal n the system acts to maxmze the utlty functon, by achevng the optmum SIR. γ opt =γ *, the soluton to Equaton (7). When two or more termnals transmt to the same base staton, all termnals n the system am for the common SIR, γ opt whch s easer to mplement [4]. In speech, the dstrbuted power control leads t globally optmum soluton. Ths s not the case n data systems. In a data system we can show that f all termnals operate wth the power levels that satsfy Equaton (7), they can all ncrease ther utltes by smultaneously reducng ther power by a small amount. The result s formally proven n [7]. 8

30 Chapter 3 Throughput Optmzaton usng Power Control and SIR balancng n a Non-Fadng Channel In ths chapter, I have taken nto consderaton the Network Asssted Power Control algorthm descrbed n the prevous secton n whch the optmum SIR s dependent upon the number of users operatng n the system. The capacty of the CDMA system plays a very crucal rule on the throughput at the base staton recever. The paper on NAPC began by lookng at the throughput of the collecton of termnals usng a common base staton. In ths secton, I have taken a general look at throughput of the base staton recever and how t s maxmzed based upon the power levels of the transcevers operatng n the wreless system. It could be shown that a good power control mechansm preserves the equal sgnal-to-nterference requrement and t acheves good results n maxmzng the overall throughput of the base staton. 3. Assumptons and Defntons: The factors descrbed n secton.. apply to ths secton too. The followng assumptons are made n ths secton: () () R b/s s the transmsson rate of the transcever and s fxed. We assume that there are 6 redundant bts beng used for channel codng. We also assume that all of these bts appear n the frame check sequence for error detecton. () (v) The number of undetected errors s neglgble. The total packet length, M = 80 bts. 9

31 3. Defnton of Termnal Throughput In ths secton, we are consderng a two-user scenaro transmttng ther data smultaneously to the base staton. Ths s the most prmtve case of a CDMA system. Accordng to assumptons () and (v) descrbed n the prevous paragraph, f bnary errors affectng the number of bts n a frame are mutually ndependent, then the probablty of successful transmsson of each termnal, f ( γ ) and s a consequence of the ndependence assumpton: f ( γ ) ( BER( γ )) M = (4) where M represents number of bts present n a transmtted frame and γ represents the SIR experenced by termnal n the system. Equaton (4) takes nto account the amount of nformaton bts beng delvered accurately to the base staton, whch depends on the SIR level of one transmtter whch n turns depends on the receved power levels of all of the sgnals but only on γ, the SIR of termnal n the CDMA system [4]. 3.3 Lterature used n the dervaton of the Bt Error Rate John J. Proaks n hs book has proven that the probablty of correct decson at the recever n the transmsson of M-ary (not to be confused wth the total number of bts n a frame) orthogonal equal energy sgnals over an AWGN channel, whch are envelope detected at the recever s gven by []: P C M = n M nξ s ( ) exp n n + ( n + ) N n= 0 o (5) 0

32 where ξ N s o s the SNR per symbol. Then, the probablty of a symbol error, whch s P M =-P C, becomes P M = M n= n+ M nξ b ( ) exp n n + ( n + ) N o (6) where ξb s the SNR per bt []. For bnary orthogonal sgnals (M = ), Equaton (6) N o reduces to a very smple form and the probablty of correct decson s gven by P b e ξ b = N o (7) Relatng Equaton (7) to the BER( γ ) n secton 3., we wll assume that the nterference has the same effect as Whte Gaussan Nose (WGN) and therefore, ξ γ = where No ξ s the receved energy per bt at the recever Dfferent Modulaton Schemes: In the context of ths study, the man effect of the modem s on the optmum sgnal-tonose rato γ opt, the soluton to Equaton (9), wth f(γ) gven by Equaton (). Table represents data for four modems descrbed n communcatons textbooks used n a nonfadng Gaussan channel: bnary phase shft keyng, dfferental phase shft keyng, coherent frequency shft keyng, and non-coherent frequency shft keyng. Table : Dfferent Modulaton Schemes Bnary PSK BER( γ ) ( ) Q γ Dfferental PSK exp ( ) γ Coherent FSK Q ( γ ) Non-Coherent FSK γ exp

33 = Q ( x) exp( u / ) du x π For our research we are usng a Non-Coherent Frequency Shft-Keyng (FSK) channel. The non-coherent recever for FSK s shown n fgure 4 below: Input H ( ω) Envelope detector t = T 0 r o H 0 ( ω ) Envelope detector Comparator r Decson: Select target t = T 0 Fgure 4: Non-Coherent detecton of bnary FSK The flters H 0 (?) and H (?) are matched to the two RF pulses correspondng to 0 and, respectvely. The outputs of the envelope detectors at t = T 0 are r 0 and r, respectvely. The nose components of output of flters H 0 (?) and H (?) are the gaussan r.v. s n 0 and n, respectvely wth σ n = σ n = σ 0 n. An orthogonal FSK s assumed here. From the practcal pont of vew n communcaton systems, FSK s preferred over Ampltude Shft keyng (ASK) because FSK has a fxed optmum threshold, whereas the optmum threshold n ASK depends on the sgnal level [3]. Hence, ASK s more susceptble to sgnal fadng than FSK. In FSK, the decson requres comparson between r 0 and r, the problem of sgnal fadng does not arse here. Ths s one of the bggest advantages that a non-coherent FSK recever have over the non-coherent ASK recever

34 and thus we choose ths model for our research. One of the bggest dsadvantages of the FSK s that t requres greater bandwdth than that of ASK []. Referrng to Equaton (4) n secton 3. n ths thess, we wll model the nterference experenced by a termnal from other termnals n the system as whte gaussan nose and hence we make use of the expresson n Equaton (7) to represent the Bt Error Rate (BER) of the channel beng used n ths research: BER( γ ) = γ 0.5 exp (8) The throughput acheved by each termnal n the CDMA system s defned as the number of correct bts receved per second by the base staton and s expressed n b/s. It s proportonal to the frame success rate gven n Equaton (4). The throughput of ndvdual termnals n the system, T be stated as follows: T = RLf (γ ) M (9) where R s the transmsson rate of each termnal n the system, and L s the nformaton bts contaned n a frame. The total throughput of the system, T, s the sum of the ndvdual throughputs of the termnals operatng smultaneously n the system N T = T = N RLf (γ ) = M = (0) Snce we are consderng a CDMA system wth only two users, substtutng N = n Equaton (0) gves us the overall throughput of the system as: 3

35 T = T = = = RLf ( γ M ) () We are tryng to maxmze the overall throughput, T, at the recever of the base staton wth respect γ for each transcever n the system. Referrng to Equaton (3) n secton..3 and usng N =, we can represent the nterference experenced by termnal, γ and the nterference experenced by termnal, γ, as follows: γ = P h GPh + σ GQ = GQ + σ () γ = Ph GP h + σ GQ = GQ +σ (3) 3.4 Throughput Optmzaton wth no Gaussan Nose n the channel Let us frst consder a system wth only two termnals transmttng to a sngle base staton located nsde the cell. We assume that the channel has no Whte Gaussan Nose or n other words σ = 0 n equatons (3), (5), () and equaton (3). The system beng looked at has fxed packet length of M bts and fxed transmsson rate of R b/s. We start our analyss by consderng a non-prortzed base system n whch all the termnals operatng n the system have equal data prorty. Then, accordng to Equaton (), the throughput of the system wth only two termnals transmttng smultaneously can be expressed as: T = M LR G f ( Gα ) + f (4) α 4

36 where γ s the SIR experenced by transcever and γ s the SIR experenced by transcever are defned as follows: Q γ = G Q Q γ = G Q (5) (6) Note that the above two equatons are derved from the defnton of γ n Equaton (3) wth σ = 0. We adopt a notaton α = above, reduces them to the followng set of equatons: Q and applyng ths to Equatons (5) and (6) Q γ = Gα (7) γ = α G (8) Substtutng (7) and (8) n (4), reduces the defnton of the throughput of the system to: T = M LR G f ( Gα) + f (9) α In ths thess, the factor LR M n Equaton (9) s assumed to be constant and thus we normalze the throughput of the system n Equaton (9) by ths factor and hence adopt a new notaton to represent the normalzed throughput of the base staton as 5

37 G V ( α) = f ( Gα) + f (30) α whch wll be used throughout ths thess. Notce from Equaton (30) that the normalzed throughput of the base staton s a functon of processng gan, frame success rate, the number of bts n a frame and the rato of transmtted powers of the transcevers. Thus, the problem beng addresses here s fndng the optmum level of the receved powers at the recever so that the throughput of the system s maxmzed. In other words, we were tryng to fnd out the optmum value of α, whch would result n maxmum number of successful transmssons. To maxmze V ( α) wth respect to α, we consder α to be a contnuous varable and dfferentate Equaton (30) to obtan V α = Gf ' G ( Gα ) + Gf' α α (3) Settng Equaton (30) = 0 and solvng for optmzaton wth respect to α gves us the followng result ' ' G f ( Gα ) = f (3) α α Note that α = satsfed ths condton. The frst pont to address n optmzng the normalzed throughput wth respect to α s whether α = represents a mnmum or a maxmum. Fgure 7 ndcates that ths depends on the value of the processng gan, G. The results of the plot wll be dscussed n the next secton. We can see from fgure 7 that the crtcal value of G needed to support 6

38 more than one user n the system n a non-prortzed based system s slghtly above 8. When G = 8, the throughput of the system stll stays below at α = and by the tme G=9, the throughput of the base staton atα = s above, thus ndcatng to us that the crtcal value of G needed to support the servces of two users s above 8. Throughout the paper, we assume that the packet that s beng transmtted between the termnals and the base staton has a length of 80 bts, or n other words M = 80. Another way of lookng at the optmum value of α needed to maxmze the throughput of the base staton s the pont that satsfes equaton (3). Fgure 5 shows the plot of f ' G ( Gα ), f, V( α ) α ' versus α when G=0. The value of G was chosen above the crtcal value as ndcated earler. One could notce from the graph that the pont where ( Gα) G f ' and f ' α ntersect s exactly and the throughput of the base staton s maxmzed at that pont where they meet. Fgure 6 shows the plot of the same functons descrbed above but the processng gan n ths case s G=6. Agan, t s clearly vsble from the plot that the optmum value of α needed to maxmze the normalzed throughput s agan. We could also observe from Equaton (3) that the optmum value of α that maxmzes or mnmzes the equaton s ndeed provded that the processng gan of the channel s well above the crtcal value. The results of the value below the crtcal value of the processng gan are dscussed n the followng secton. Through the plots n fgures 5 and 6, we have confrmed that = α s the pont where the local maxma of ( α) V les and hence the base staton throughput s maxmzed at ths pont. Two other nterestng ponts to be looked at would be the two extreme values of α = 0,. 7

39 Optmzaton of Throughput T ( α ) g ( α ) g ( α ) α, α, α alpha Fgure 5: Plot of ( Gα) G f ', α f ', ( α ) T vs α when G = 0 Optmzaton of Throughput T ( α ) g ( α ) g ( α ) α, α, α 3 alpha Fgure 6: Plot of ( Gα) G f ', f ', T ( α ) vs α when G =6 α 8

40 Graph of Normalzed Throughput versus α (M = 80).8 Normalzed Throughput G = 64 G = 6 G = 9 G = 6 G = G = 4 0. G = α Fgure 7: Optmzaton of base staton throughput versus α ( β = ) 3.4. Analyss of the system wth no Whte Gaussan Nose Fgure 5 represents the plot of V ( α) vs α for values of α between 0 and. The plot when presented on a logarthmc scale s symmetrc for values of α > because V α ( α ) = V. The observatons that could be made from the plot are as follows: Intally, when α =0, transcever s the only transmttng termnal n the system and the throughout of the system starts off at snce t s the lone termnal n the system. When G s low, the system does not have suffcent bandwdth to support two termnals and α = 0 leads to hgher throughput than α =. Wth α = 0, P =0 and 9

41 termnal transmts wthout nterference producng V(0) =. In order for the system to allow two termnals to transmt ther data smultaneously, the processng gan of the channel has to be ncreased. Increasng the processng gan ncreases the bandwdth of the channel. By ncreasng the bandwdth of the channel, we ncrease the capacty of the system and hence more termnals wll be able to operate n the system smultaneously as the value of G keeps on ncreasng. Fgure 7 suggests to us that for values of G < 8, one of the two termnals has to shut off ts power and let the other termnal use the system all the tme. When the value of G s greater than crtcal value 8, the fgure shows that the throughput of the system starts rsng above and approaches (the maxmum value of V (α ) ) asymptotcally as G approaches. Ths gves us an ndcaton that as the number of chps beng used for the channel starts rsng above 8, the bandwdth of the system s able to let two termnals transmt ther data smultaneously to the central base staton located nsde the cell. Thus, when G s hgh, there s suffcent bandwdth to support two termnals. In ths case V() = f(g) >. In the lmt as G ncreases wthout bound V (). When G > 8, t can be seen that the optmum value of α needed to maxmze the throughput of the system s equal to, at whch pont of tme the two termnals n the system operate at equal powers. Thus, as the bandwdth of the system ncreases, more and more users can be ncorporated nto the system due to more network resources becomng avalable. 30

42 An nterestng ssue s the value G = G crtcal such that for G < G crtcal, = V(0) > V() and for G > Therefore, G crtcal, = V(0) < V(). At G = G crtcal : G crtcal satsfes the equaton = V(0) = V() = f ( G) ( G) f = or f ( G) =. (33) For BER gven n Equaton (8) and M = 80, ths processng gan s G crtcal =8. The method that was used n calculatng the value of below n ths thess. G crtcal s shown n secton 5.3 Confnng our attenton to nteger values of G, we fnd that for G 8, V(0) > V() and the system throughput s hghest when termnal turns off ts transmtter. However, for G 9, V (α ) s a maxmum at α =. In ths case t s best to have Q = Q n whch case both the sgnals arrve at the base staton wth = V α equal power. Because ( ) V α by comparng V ( ) wth ( ) system wth no nterference., we could have performed the same analyss V. Wth α =, P = 0 and thus termnal uses the 3.5 Conclusons One could derve from the above analyss that as long as the value of G>8, the system s able to support more than one user and as long as the receved powers of the termnals at the base staton recever are equal, the overall throughout of the system s maxmzed. At 3

43 ths pont, the two termnals utlze the network resources properly, hence maxmzng the performance of the cellular system. Ths s a very mportant aspect n desgnng cellular communcaton models snce the moble servce provders promse ther customers to offer them wth the best qualty of servce and hence the network engneers have to desgn such networks very carefully snce there are a lot of changng parameters n cellular communcatons. A change n one parameter can adversely affect the performance of the cellular system and hence a lot of research needs to be put n before desgnng an optmal cellular network. A cellular network desgn conssts of all the parameters that are needed to provder a customer wth a low blockng probablty, hgher QoS, less usage of battery power, lower call droppng probablty, lower sgnal-tonterference rato and much more. All these objectves have to be kept n mnd n desgnng a cost-effectve cellular network. In ths secton we have addressed the problem of adjustng the receved power levels at the base staton recever n order to mnmze the sgnal-to-nterference rato among the termnals operatng n the system. By havng a lower sgnal-to-nterference rato, the probablty of successful transmsson ncreases, as fewer packets wll be dropped because there s not too much nterference from the nterferng termnal. The probablty of successful transmsson depends heavly on the processng gan (G) of the channel. The probablty that the packets wll be successfully delvered to the base staton for dfferent values of G when the two users are transmttng at equal powers s presented n the Table : 3

44 Table : Comparson of G and f ( γ ) Processng Gan(G), number of chps used Probablty of Successful transmsson f ( γ ) e Thus, once could see from Table that as the number of chps used for channel codng ncreases, the probablty of successful transmsson also ncreases. In other words, the greater the bandwdth of the channel, the greater s the probablty of nformaton beng delvered to the base staton accurately. The overall throughput of the system ncreases wth ncreasng G and approaches a maxmum value of as G. Thus as long as the termnals adjust ther powers accordngly and the receved powers of the termnals are equal, the maxmum amount of data s delvered accurately to the base staton wth mnmum errors. Note that n ths secton we have consdered a closed loop power control algorthm n the reverse drecton n whch the base staton calculates the receved power levels and transmts them back to the termnal tellng the termnals n the system to adjust ther power levels accordngly such that the termnals operates wth mnmal power and at the same tme maxmze the sgnal to nterference rato. The next chapter looks at 33

45 optmzaton of throughput of the system n the presence of Gaussan Nose. We wll stll consder a system wth non-prortzed termnals operatng smultaneously. 34

46 Chapter 4 Throughput Optmzaton n a CDMA network va Power Control n the Presence of Whte Gaussan Nose 4. Introducton to Sgnal to Nose Rato (SNR) The above results were based upon the assumpton that there s no Gaussan nose present n the channel. But n practcal systems, all channels and recever crcuts contan nose of some sort, whch affects the performance of the transmsson of data from the transmtter to the recever. The rato of the magntude of the wanted sgnal to that of unwanted nose can be expressed n smple arthmetc rato called the Sgnal-to-Nose Rato (SNR). In order to understand the effects of nose n communcaton networks let us take a smple example. Suppose we take a mcrophone and connect t to an osclloscope tuned approprately. The emtter s put a few centmeters away from the mcrophone. When the emtter s swtched off, the osclloscope wll show a straght lne, no sgnal. When the emtter s swtched on, the osclloscope wll show a sne wave. Suppose now that we put the emtter four tmes (nverse square law) farther from the mcrophone. When the emtter s on, the sgnal shown s two tmes weaker and hence by ncreasng the amplfcaton of the osclloscope we can vew the sgnal properly. As we keep on movng the emtter away from the mcrophone, the nose present n the system starts chppng n and ths could be clearly observed when the emtter s turned off. When the emtter s at a consderable dstance from the mcrophone and s turned off, we wll stll some waves on the osclloscope, whch s caused due to the nose n the system. When the emtter s turned on, the sne wave smply adds tself to nose. The nose n the system remans the same whether the emtter s turned off or on. 35

47 4. Sgnfcance of SNR n Communcaton Channel In wreless system where we have a transmtter and a base staton, the transmtter plays the role of the emtter and the base staton plays the role of the mcrophone. As the termnals n the system move away from the base staton, the receved power of the termnal at the base staton decreases along wth the dstance. Wreless systems are partcularly dffcult to desgn due to the sgnals hgh vulnerablty to nose nterference, and changng channel condtons [9]. Under such crcumstances the throughput of the system becomes an mportant factor. There are many factors that nfluence the throughput and hence are there are many dfferent approaches that can be taken to maxmze t [9]. Choosng an optmum power level to maxmze the throughput n presence of nose has been nvestgated here. As descrbed earler n ths paper, the SIR experenced by transcever and transcever wth no nose power n the base staton recever s gven by equatons (5) and (6). When there s nose n the base staton of the recever the sgnal-to-nterference nose rato (SINR) experenced by transcever s defned as follows: γ = Ph G = G (34) P h + σ Q + σ Q Dvdng (34) by Q smplfes the equaton to γ Q G Q = (35) σ + Q 36

48 Let us adopt the notaton that σ Q =. Thus the SINR experenced by transcever SNR from the transmsson of transcever and nose power n the channel reduces (35) to the followng form γ = Q G Q + SNR (36) Usng the earler defnton ofα Q = Q, smplfes equaton (36) to G α SNR G α SNR γ = = (37) + SNR + SNR In a smlar manner the SINR experenced by transcever n presence of nose can be shown as follows: G G SNR γ = = (38) α + α SNR + SNR Notce that when SNR ->, equatons (37) and (38) reduces to equatons (7) and (8) whch comples wth our results when we consdered a system wth no Gaussan Nose n the channel. Thus, the normalzed throughput of the base staton can then be expressed as: G α SNR G SNR V ( α ) = f + f, 0 Q Qmax ; 0 α (39) SNR + α SNR + It would be nterestng to fnd the optmum value of α that s needed to maxmze the overall throughput of the base staton n the presence of Whte Gaussan Nose. Dependng on what the value of SNR s, the throughput of the base staton wll vary 37

49 accordngly and the crtcal value of processng gan, G crtcal, needed to support more than one user n the system has to be hgh where there s too much nose n the channel (lower SNR) and low when there s less nose n the channel (hgh SNR). Fgure 8 below starts off by showng the plot of normalzed throughput of the base staton versus α when SNR=. Normalzed Throughput Graph of Normalzed Throughput versus α n the present of AWGN (SNR=) G=8.8 G=0 G= G=.6 G-4 G=6.4 G=0 G= α Fgure 8: Plot of normalzed throughput versus α (SNR=) 38

50 Fgures 9 through 3 represents the same plot as above but for dfferent values of SNR. Normalzed Throughput Graph of Normalzed Throughput versus α n the present of AWGN (SNR=) G=4 G=8 G=0 G= G= G=4 G=6 G= α Fgure 9: Plot of normalzed throughput versus α (SNR=) Normalzed Throughput Graph of Normalzed Throughput versus α n the present of AWGN (SNR=5) G=4 G=8 G=9 G=0 G= G=6 G= α Fgure 0: Plot of normalzed throughput versus α (SNR=5) 39

51 Normalzed Throughput Graph of Normalzed Throughput versus α n the present of AWGN (SNR=0) G=.8 G=4 G=8.6 G=9 G=0.4 G= α Fgure : Plot of normalzed throughput versus α (SNR=0) Graph of Normalzed Throughput versus α n the present of AWGN (SNR=50) Normalzed Throughput G= G=4 G=8 G=9 G=0 G= α Fgure : Plot of normalzed throughput versus α (SNR=50) 40

52 Graph of Normalzed Throughput versus α n the present of AWGN (SNR=00) Normalzed Throughput G= G=4 G=8 G=9 G=0 G= α Fgure 3: Plot of normalzed throughput versus α (SNR=00) 4.3 Analyss of the Plots Fgure 8 represents the plot of the base staton throughput versus α when SNR=, thus sgnfyng that the nose power n the channel s equal to the receved power of the transmtter and hence t would greatly effect the throughput of the base staton. We can see from the plot above, for values of G 0, the base staton throughput remans below. Ths tells us that as long as the value of the processng gan of the channel s less than 0, only one termnal n the system can operate whle the other turns off ts transmtter. Infact the plot conveys to us that the performance of the lone termnal under heavy nose condtons s not very sgnfcant and t does contrbute much to the base staton throughput. One could 4

53 observe from the plot than when G s small, the contrbuton of the lone termnal to the throughput s not that sgnfcant and the throughput starts off at a value near 0.5 when G = 8 and very quckly approaches 0. Thus n order for the lone termnal to perform better under heavy nose condtons, the processng gan of the channel need to be ncreased so that enough resources can be allocated for the termnal to transmt ts data accurately. The plot tells us that n order for the lone termnal to perform better the mnmum value of processng gan needed s G=0 whch s farly hgh. Hence n ths case, G crtcal =0. If both the termnals try to transmt ther data smultaneously to the base staton, both wll nterfere wth each other s transmsson and there wll be a lot of bt errors caused and hence the performance of the network wll degrade very drastcally. Under such condtons, the nformaton bts of both the termnals wll not be delvered accurately to the base staton. As the value of G > Gcrtcal, the throughput of the base staton recever starts ncreasng and rses above. Thus, the processng gan of the channel needs to be ncreased n order for both the termnals to operate wth equal powers and mnmum nterference from each other. One could see from the plot that when G =3, reasonably hgh, the base staton throughput s maxmzed when α =. Hence, we arrve at the concluson from the plot that when there s a lot of nose present n the channel and only one termnal s transmttng, the nose n the channel prevents the termnal to operate wth maxmum effcency for lower values of G. Hence, to maxmze the throughput of the base staton, the value of G needs to be ncreased to a farly hgh level (0) n order to provde the termnal wth enough network resources and bandwdth. For values of G 8, the 4

54 throughout of the base staton s 0 snce G s very low and hence are not presented n the plot. When G > Gcrtcal, the system s able to ncorporate more than one termnal and as the value of G keeps on growng, both the termnals are able to operate wth maxmum effcency, thus maxmzng the throughput of the base staton at α =. Fgure 9 represents the plot of throughput of the base staton versus α but now the value of SNR=, whch s not a very sgnfcant mprovement over the prevous value. The nose present n the channel s stll very hgh and hence we expect the value of G needed to ncorporate the transmssons of two termnals to be farly hgh. It could be observed from the plot that as long as G 4, the system s much better off by lettng only one of the termnals transmt n the system. When G=4, the throughput of the base staton shows an mprovement and the system s able to ncorporate the transmsson data of the second termnal. Observe that when G = 4 (not shown n fgure 9), the throughput of the base staton starts off at a value near 0.5. Hence n order for the one termnal to perform better, the value of G needs to be ncreased thus provdng the termnal wth enough network resources. When G=8, termnal operates wth maxmum effcency ( V ( α) = ; α = 0 ) but when termnal turns on ts transmtter power, because of unavalablty of bandwdth, t causes a lot of nterference to the second termnal causng the throughput of the base staton to fall down to 0. Hence, we could say that G crtcal=4 n ths case. When SNR=5, t could be seen from the plot n fgure 0, G crtcal s a bt below because at G=, the throughput of the base staton stablzes and does not fall off 43

55 the threshold value of. We could see from the plot that when G=0, the throughput of the base staton ntally stays below but s barely able to make t above for values of α near. As the value of G ncreases, the base staton throughput also ncreases and gets maxmzed when α =. Thus the system performs better as G ncreases. In a smlar manner, when SNR=0, one could expect the value of G crtcal to reduce snce the nose n the channel s decreasng and hence there wll be less errors made n the transmsson of nformaton bts of the termnals to the base staton. When SNR s very hgh such as SNR=50, 00 n fgures and 3 respectvely, we observe that G crtcal reduces by a bg amount and the system s already better off when G = 9 and the base staton throughput s maxmzed when α =. Ths s very obvous because hgher values of SNR sgnfy lower nose power n the channel and hence we do not need a hgher degree of codng to protect the nformaton bts from beng corrupted or damaged. The bandwdth necessary to allow the successful transmsson of two termnals n the system s acheved when G s qute low. Thus the general concluson that can be drawn from the plots presented above s that when SNR s very hgh, the nose n the channel s hgh and hence the processng gan of the channel needed to allow two termnals to smultaneously transmt ther data s very hgh snce we need better codng and protecton. When SNR s low, t s close to stayng that there s no nose n the channel and hence the system s able to allocate enough network resources to both the termnals for 44

56 lower values of G and the system performs wth greater effcency. In every practcal network, the engneer of the system tres to mantan the SNR level as low as possble and the reason to do that s presented above n the plots. Snce we already know that the optmum value of α, α opt, needed to maxmze the throughput of the base staton s, t would be nterestng to plot the throughput of the base staton wth respect to SNR for α = dfferent G. Fgure 4 below presents such a plot when SNR = 4. Graph of throughput versus SNR (M=80) α = G =64 Normalzed Throughput of the system α = G =6 α = G =0 α = G =8 α = G = SNR Fgure 4: Plot of Normalzed throughput versus SNR 45

57 4.4 Analyss of the Graph of V versus SNR In the earler chapter, based upon the results we came to a concluson that n order to maxmze the throughput of the base staton, the receved power levels of all the termnals must be equal and hence n ths plot we have assumed α = and the results are based upon that. The followng conclusons could be drawn from the plot of the throughput of the system versus SNR: It could be seen that as the SNR ncreases for values of G < 8, the throughput of the system never qute actually rses above snce the network resources are not suffcent enough to support a system wth two users snce they requre a larger bandwdth. We could also observe that for lower values of SNR close to zero, the systems throughput s almost zero snce the network resources are under-utlzed suggestng that the network s better off by lettng only one termnal operate n the system. Thus, we could conclude that for lower values of processng gan, only one user can use the system untl there s enough bandwdth avalable for the second user to transmt ts data to the base staton. For values of G 8, the throughput of the system ncreases as the sgnal to nterference nose rato of the system ncreases and hence the network s able to ncorporate the transmsson bts of two termnals n the system and let them transmt at equal powers but the throughout does not qute reach the maxmum value, untl the value of G gets closer to 6. It could be observed that n order to allow more and more termnals to share the system and at the same tme maxmze the throughput of the system, the number of chps beng used should be ncreased above the crtcal value of G=8. 46

58 The throughput of the system starts reachng the maxmum value and s approxmately flat near the hghest value at whch pont more and more users can begn to share the system and make effcent use of t. Thus, the results agree wth our prevous results that we obtaned earler n the paper. The level of sgnal to nose rato for values of G 6 should be hgh enough n order to let the two termnals transmt at equal powers and at the same tme maxmze the throughput of the system. More number of are users are allowed to use the system at ths pont. The results we obtaned here are very smlar to the results we obtaned n secton 4.3 earler. The reader should be able to see that when SNR s too low, the nose power s hgh n the system and hence the value of G needed to support more than one termnal should be very hgh. G = 8 s the crtcal value when we have a hgh SNR rather than a low SNR. When both the termnals n the system operate at equal powers, the normalzed throughput of the base staton reduces to the followng equaton: Note that when SNR 4.5 Conclusons G SNR G SNR G SNR V (α ) = f + f = f (40) SNR + ( + SNR) + SNR, Equaton (40) reduces to (33). In a smlar manner, V ( ) = V 0) = f ( G SNR) ( (4) In ths chapter, we have shown the effects of SNR on the throughput of the base staton and looked at the system for dfferent values of SNR. Some general conclusons can be 47

59 drawn from the plots that we have seen n ths chapter. We have seen that when the SNR of the system s very low, the nose n the channel s very hgh and hence n order for the system to protect the nformaton bts of the two termnals and transmt ther nformaton successfully to the base staton, the processng gan of the channel should be hgh. In a smlar manner, when there s less nose n the channel, SNR s hgh, the value of processng gan needed to support the servces of more than one user s not very hgh and the network s able to provde the termnals wth enough resources to transmt ther data at the same tme. However, the optmum value of α, α opt, needed to optmze the throughput base staton s stll provded that the value of SNR s hgh. The receved power levels of the transcevers n the presence of whte gaussan nose are not affected sgnfcantly provded the network has enough resources avalable to support more than one user n the system. The nose plays a very mportant role n communcaton networks and may affect the system s performance. Note that the upper bound on the number of user n the system s stll bounded by Equaton (3). If the number of termnals operatng n the system crosses the boundary gven by Equaton (3), the network performance s drastcally degraded and the network resources wll be over utlzed. Ths would result n an unstable network. Transmsson of packets successfully to the base staton becomes a very mportant ssue when there s nose present n the channel. If there s too much whte gaussan nose avalable n the channel, the packets of nformaton mght not be delvered accurately whch results n retransmssons of packets and ths mght affect the performance of the network sgnfcantly. The next chapter looks nto a CDMA system n whch dfferent transcevers are gven unequal nformaton prorty. 48

60 Chapter 5 Throughput Maxmzaton n a CDMA network va Power Control of Transcever wth Dfferent Prortes 5. Introducton In the prevous chapters a fxed nformaton rate has been typcally been assumed, and an optmal power vector has been sought. A transcever s processng gan and SIR are equal partners n determnng the probablty of success of a packet transmtted from or to the transcever. Furthermore, a transcever s contrbuton to the system s throughput ncreases monotoncally wth the frame success probablty to the processng gan []. Hence, both transmt power levels and processng gan should be optmzed smultaneously. In the work below we show that even f the contrbuton of each transcever to the network throughput s weghted dfferently, through a lnear combnaton (whch would reflect a stuaton n whch bts from dfferent users are valued dssmlarly by the system admnstrator) stll they should am for the same effectve SIR. Thus, an nterestng area of research n the feld of wreless communcatons s how the power should be allocated between the dfferent transcevers n a system where each transcever has a dfferent nformaton prorty than other. In practcal systems, every user wants to have hs/her data to be delvered accurately and faster to the base staton and the Qualty of servce offered by the network s very mportant. A user certanly wants to have a certan degree of prorty gven to ther moble termnal whle transmttng data to the base staton. The user mght be wllng to nvest more money n order to get a hgher degree of performance. Dfferent cellular subscrber companes offer dfferent rate plans, whch provde the user wth a better degree of transmsson effcency. If a partcular moble subscrber s wllng to pay more, hs/her termnal wll 49

61 be gven a hgher nformaton prorty as compared to other termnals n the system. Hence, dfferent telephone companes offer dfferent compettve rate plans to ther subscrbers promsng them to offer a better qualty of servce as compared to other telephone companes. Ths keeps the competton gong n the market and day by day there has been a growng popularty among the people tryng to own a cell phone. If a customer s provded wth a better qualty of transmsson, then he/she wll be defntely wllng to nvest ther money n that partcular rate plan and hence we got the motvaton to explore the system n whch dfferent termnals are gven unequal nformaton prortes. It s obvous that f one termnal has a hgher nformaton prorty than the other, then t wll have better access to the base staton as compared to others. It would be nterestng from an engneerng pont of vew to explore how do the termnals adjust ther power n order to maxmze the overall weghted throughput of the system, hence ncreasng the system effcency. 5. Throughput Optmzaton n a Prorty Based System The followng secton looks at the throughput optmzaton n a CDMA system where one termnal s gven a hgher nformaton prorty compared to other termnals nformaton. The assumptons are the same as made n the prevous chapters. An deal transmsson of corrupted packets s assumed n ths secton. We are consderng a CDMA system n whch every termnal s transmttng to the base staton at the same transmsson rate, R. The number of bts that are transmtted n one packet of data s agan consdered to be constant, M = 80 bts. Hence, referrng back to Equaton (9), the weghted throughput of termnal havng an nformaton prorty, β s gven by 50

62 T β RL ( γ ) = f (4) M where β s the weghtng coeffcent, reflectng the possble fact that the system s admnstrator may make a value of a transcever s contrbuton to the network throughput dependent upon the specfc user and γ s the sgnal-to-nterference rato experenced by the partcular termnal from other transmttng termnals n the system. Thus, the aggregate throughput of the system n whch two termnals transmt ther data wth unequal nformaton prorty s gven by: T = T = = = RLβ M f ( γ ) RL = [ β f ( γ ) β f ( )] M + (4) γ Snce M RL s a constant, t does not affect the optmum power level rato. Thus we defne the normalzed throughput: ( γ ) f ( ) V ( α) = β f + γ (43) Let us consder a very prelmnary form of the above equaton n whch transcever s gven twce the nformaton prorty as compared to the transmsson prorty gven to transcever. Hence, β = β where β s the nformaton prorty of transcever and β s the nformaton prorty of transcever transmttng ther respectve data s to a sngle base staton located nsde the cell as the termnals. If we assume β =, then β beng twce as large as β gves us the value ofβ = and hence equaton (43) can we re-wrtten as 5

63 where γ G V ( α ) = [ f ( γ ) + f ( γ )] = f ( G α ) + f (44) α γ and are gven by Equatons (7) and (8). We try to optmze ( α) V wth respect to α, the rato of the transmtted powers of the two termnals. In order maxmze V wth respect to α, we have to take the partal dervatve of V ( α) n Equaton (44) wth respect to α and set t equal to 0. V α = 0 (45) Takng the partal dervatve of V wth respect to α gves us the followng equaton G Gf ' V α = f ' ( Gα ) G (46) α α Thus, n order to optmze the throughput, we set the above equaton to 0. In dong so we get G f ' α α = f ' ( Gα ) (47) Hence we see that unlke Equaton (3), α = does not guarantee that the frst dervatve s 0. Therefore, the normalzed throughput wll be maxmum when Q Q. We expect that the optmum α >, and Q > Q because termnal has a hgher prorty and hence t should have more powerful receved sgnal than termnal. The frst dervatve does not gve us much nformaton because the soluton to the above equaton ** α could be a local maxmum or local mnmum. A suffcent condton for a local maxmum throughput at ** α = α s: 5

64 V α α = α ** < 0 (48) 5.. Performance Analyss Fgure 5 represents the plot of throughput of the system versus a for dfferent values of a between 0 and 0. We can see from the fgure that when α = 0and when α =, the system conssts of a lone termnal and that s the only termnal contrbutng to the throughput of the base staton recever. We can see from the fgure when G s below a certan threshold value, the CDMA system s able to provde servce to only one termnal n the system snce t has not enough bandwdth to support the servces of the other termnals n the system. Intally, when G s below the crtcal value of G needed to support two users, the system s not able to provde suffcent bandwdth to let two termnals transmt smultaneously and hence the throughput of the base staton drops down drastcally and approaches zero. The plot tells us that when the processng gan (chp rate) of the channel s not hgh enough to support two users, only one termnal be allowed to use the system wthout any nterference and n ths case t would be termnal ( α =, P = 0). Thus α = leads to a hgher throughput than α = for low values of G < G crtcal. We defne G crtcal as the mnmum value of G needed to satsfy the equaton: V() = V( ) =. It s easy to acheve ( α) = V by lettng P = 0, α =. The real queston s what processng gan s needed to have V ( α) >? By achevng V ( α) > can have the two transmtters share the system smultaneously. Fgure 5 suggests that G 9 s necessary. Wth G=9, β =, the system s able to support two termnals wth unequal power because V > = V ( ). However, wth equal power V() <. max, we 53

65 However, wth G=9, α = s no good snce the throughput of the base staton s below and hence we can get better results for throughput by lettng α =. Thus the system would be better off by lettng only one termnal transmt. But one could observe from fgure 5, when G=0, ( ) > V ( ) V. Thus we can say that G crtcal n ths case s 0 and the method of calculatng t s shown n the future secton. We can argue that the value of G crtcal accordng to the defnton defned above s not exactly 0 but slghtly above 9. We round up G to the nearest nteger to make sure that V ( ) V ( ) crtcal. As the system s chp rate ncreases, the capacty also ncreases and hence the system wll be able to provde servces to more than one user. Smlarly, the plot tells us when α, termnal has to shut off t s power and termnal be allowed to transmt t data snce as α grows, termnal transmts at a much hgher power than termnal and hence t would cause a lot of nterference to termnal and ths would affect the throughput of the base staton. Under such crcumstances, the probablty of successfully transmttng the packets of termnal declnes and t would not be benefcal for termnal to transmt ts data and hence t has to turn off t s power. Thus the throughput of the system stablzes to n the long run and the system effcency s mantaned. 54

66 3 Graph of Normalzed Throughput versus α (M = 80) G=6 G=64.5 G=0 Normalzed Throughput.5 G=9 G=8 G=6 G=4 0.5 G= α Fgure 5: Plot of normalzed throughput versus α ( β = ) We sad earler that as long as the processng gan of the channel s below a certan threshold, only one of the termnals s allowed to use the system. An engneer s always nterested n knowng the crtcal value of G above when the two transcevers can transmt ther data successfully to the base staton. If one pays a closer attenton to the plot presented n fgure 5, we could see that the value of G needed to support more than one user s 9. As the value of G starts ncreasng above 9, the network throughout starts gvng us postve results (rsng above ) and hence the system s able to provde resources to more than one termnal and they are allowed to operate smultaneously. Notce that the value of α needed to optmze the throughput s stll close to and gets closer and closer to as G ncreases. 55

67 One could observe that we arrved at smlar conclusons as dscussed n chapter 3. Thus, as long as the value of G < G crtcal, n ths case 0, the system s able to support one of the users snce there s not enough bandwdth avalable to let two termnals transmt ther data smultaneously. As the value of the processng gan, G starts ncreasng and crosses the crtcal value, we can observe from the plot that the throughput of the system starts rsng gradually above for ncreasng values of G and approaches 3, the maxmum value of V(α ). Thus the crtcal value of G needed to support more than one user n the system where one of the termnals has twce the nformaton prorty as compared to other termnal s G crtcal = 0. We could see that as the processng gan ncreases, the maxmum value of the throughput keeps on rsng and gets very close to 3. Practcally, t wll never touch 3 snce not all system are deal n nature. Due to the ncrease n G and the bandwdth of the channel, the capacty of the system keeps on ncreasng and for hgher values of G, the system can support more and more users The optmal value of α needed to optmze the system performance s stll very close to and as G ncreases, t moves closer and closer to. Fgure 6 through 8 presents the plot of normalzed throughput of the base staton versus α for values of G=8, 9 and 6. If one blows up the graphs at ponts where V ( α) approaches the maxmum value, one could observe that the value of α needed to maxmze the throughput les n the vcnty of for value of G = 9 and as the processng gan ncreases, the pont moves closer and closer to and at hgh values of processng gan t s exactly. Table 3 below lsts the optmum values of α and the correspondng value of * f ( γ ) and ( ) f for dfferent values of G. γ 56

68 .5 Graph of Normalzed Throughput verusu α (β = G=8 M=80) Normalzed Throughput.5 N. Thpt user user α Fgure 6: Plot of normalzed throughput vs α ( β =, G = 8).5 Graph of Normalzed Throughput verusu α (β = G =9 M =80) N. Thpt user user Normalzed Throughput α Fgure 7: Plot of normalzed throughput vs α ( β =, G = 9) 57

69 3.5 Graph of Normalzed Throughput verusu α (β = G=6 M=80) N. Thpt user user Normalzed Throughput α Fgure 8: Plot of normalzed throughput vs α ( β =, G = 6) Table 3: Maxmum values of Overall Throughput and throughput of ndvdual termnals G α opt max T * f ( γ ) max ( ) max f γ

70 5.3 Relatonshp of Informaton Prorty, β to Processng gan, G In the prevous secton, we saw that the value of processng gan needed to provde network resources to allow transmsson of more than one termnal to a sngle base staton s dependent on the nformaton prorty factor, β gven to transcever. The necessary value of G ncreases as β ncreases and ths s clearly evdent based upon the plots that we showed you earler. In ths secton, we try to establsh the relatonshp that exsts between β and G. In order to so, we follow the followng procedure descrbed below. The conclusons presented below are based upon the observaton so far As a?8, we adopt the notaton of representng the throughput of the system by ( ) V. Substtutng the value of a = 8 n (43) by assumng β and = representng β = β, the throughput of the base staton recever s gven by the equaton below ( ) = β V (49) When a =, all the transcevers operate wth equal sgnal-to-nterference rato and hence we presume that γ = = γ γ T. Pluggng n the value of a and β = β, β n (43) reduces the equaton of the normalzed throughput of = the base staton recever and thus G V ( ) = ( β + ).5exp (50) M 59

71 Thus, we arrve at the concluson based upon the equatons (49) and (50) that for values of G < 8, V ( ) > V ( ) approaches, V ( ) > V ( ). In a smlar manner as the value of G starts ncreasng and. The two equatons suggest to us that as long as the processng gan of the channel stays below G crtcal and the rato of the receved power of the two termnals s greater than and approaches ( Q = 0 ), the overall throughput of the system approaches the value of the nformaton prorty gven to termnal, β. An nterestng queston that arses from the above dervatons s what crtcal value of the processng gan (G crtcal ) s needed so that the throughput of the base termnal recever of a system wth only one termnal transmttng s equal to the throughput of the base staton recever wth two termnals operatng at equal powers ( V ( ) =V ( ) ). Remember the defnton of G crtcal from secton 5..? The answer to ths queston would help us n establshng a drect relatonshp between the processng gan, G and the nformaton prorty, ß. In other words, our goal s to fnd the crtcal value of the processng gan (G crtcal ) of the channel, the soluton to the equaton V ( ) = V ( ). And the soluton of the equaton depends on the value of the nformaton prorty ndex, ß. Therefore, n order to fnd the value of G crtcal, we have to solve the followng equalty for G crtcal n terms of β and M. G ( ) crtcal β = β +.5 exp (5) M 60

72 Solvng equaton (5) for G crtcal gves us the followng result: ln G crtcal = M β β + (5) Equaton (5) gves us a lot of nterestng nsghts nto the system beng looked at. The rght hand sde of the equaton provdes us wth some valuable nformaton. One could see n Equaton (5), that the crtcal value of the processng gan, G crtcal, s ndependent of the powers that the termnals are operatng at and s dependent on the value of the nformaton prorty gven to the termnals, ß, and the packet sze, M, beng transmtted by the termnals to the base staton. In our prorty-based system, we assgn termnal twce the prorty than termnal. Substtutng, ß= and M = 80 bts n Equaton (5) and roundng up the result to make sure that ( ) V ( ) V gves the value of G crtcal=0, and hence ths comples wth the results we obtaned through our plots earler, whch showed that the crtcal value of the channel processng gan needed to support more than one user n a prorty based system ( β = ) was 0. In a smlar manner, when we substtute ß= and M= 80 n Equaton (5), we obtan G crtcal = 9 whch agan proves the results we obtaned n fgure 7. Fgure 9 plots the processng gan, G versus the nformaton prorty, ß. Notce that as the value of ß grows, the optmum value of G needed to support more than one termnal n the system also ncreases wth t. A greater nsght nto the plot reveals that the theoretcal results obtaned earler for value of ß= and agrees wth the plot. The graph also shows that as the prortes of the termnals n the system ncreases; the processng gan of the channel also ncreases along wth t snce a greater network bandwdth s 6

73 needed to support more than two termnals operatng wth mnmum nterference from other termnals n the system. Fgure 9: Relatonshp between Processng Gan and β Table 4 lsts the values of β and the correspondng values of G needed to support the load of two termnals transmttng smultaneously to the base staton. Table 4: Relatonshp of G crtcal (rounded up) and β β G crtcal